Resurrections, a method of human transmutation, only has a problem with the soul. Since it is gone, you cannot call it back. Think of it like a chemical change, e.g. burning paper, you cannot restore it. The only real successful attempts of human transmutations are the homunculi though, but they still need souls too. To make up for the lack thereof, they run on Philosopher's Stones, which incidentally is made from trapped souls.
So Human Transmutation is possible. Just not all methods will achieve desired intent.
This is really simplified from memory of the show but should get the point across.
Alchemy is still used medicinally. You could argue that without Truth punishing people attempting to reclaim souls that at best they would just craft human shells or fresh corpses (as weird as that sounds). Remember, this is basically high-speed 3D printing.